Faraday waves on a bubble-trapped Bose-Einstein-condensed binary mixture

By studying the dynamic stability of Bose-Einstein-condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the s-wave contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov-de Gennes and Floquet methods, with predictions being analyzed by full numerical solutions applied to the corresponding time-dependent coupled formalism.